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Chapter 2

Chapter 2 . Analyzing Data. Section 2.1 Units and Measurements. Systeme Internationale d’Unites (SI) is an internationally agreed upon system of measurements. A base unit is a standard. . Section 2.1 Units and Measurements. Section 2.1 Units and Measurements.

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Chapter 2

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  1. Chapter 2 Analyzing Data

  2. Section 2.1 Units and Measurements • SystemeInternationaled’Unites (SI) is an internationally agreed upon system of measurements. • A base unit is a standard.

  3. Section 2.1Units and Measurements

  4. Section 2.1 Units and Measurements

  5. Section 2.1 Units and Measurements • Standard Units…… • Length=Meter • Time=Second • Temperature=Kelvin • Mass=Kilogram

  6. Section 2.1 Units and Measurements (MASS) • A kilogram is too large for our minute experiments, so we commonly use the gram. • Balance- How we measure mass. • WE DO NOT WEIGH OBJECTS, WE FIND THE MASS!!!!!!!!!!!

  7. Section 2.1 Units and Measurement (temperature) • Temp measures how hot/cold. • SI UNIT=Kelvin, but we use Celsius. • 0°C=Freezing point of water • 100°C= Boiling point of water • 0K= ABSOLUTE ZERO (unattainable) • K= °C + 273 °C= K-273 • °C = (F-32)(5/9) F= (9/5) °C +32

  8. Section 2.1 Units and Measurements • Not all quantities can be measured with SI base Units. • A unit that is defined by a combo of base units is called a derived unit. • EXAMPLE OF DERIVED UNIT= cm3 or dm3.

  9. Section 2.1Units and Measurements • cm3 = mL • dm3= L • Density is a derived unit. • Density= Mass/Volume

  10. United Streaming Video • Matter and its Properties-Measuring

  11. Section 2.2Scientific Notation and Dimensional Analysis • Scientific Notation can be used to express any number as a number between 1 and 10 (the coefficient) multiplied by 10 raised to a power (the exponent) • 6x105

  12. Section 2.2 Scientific Notation • The Number of places moved equals the value of the exponent. • Exponent is POSITIVE when moved to LEFT • Exponent is NEGATIVE when moved to RIGHT 800= 8.0 x 102 0.0000343= 3.43 x 10-5

  13. Section 2.2 Scientific Notation - Addition and Subtraction • Exponents MUST be the same. • Rewrite values with the same exponent • Add or subtract coefficients.

  14. Section 2.2 Scientific Notation • Multiplication and Division • To multiply, multiply the coefficients, then add exponents. • To divide, divide the coefficients, the subtract the exponent of the divisor from the exponent of the dividend.

  15. Section 2.2 Dimensional Analysis • Dimensional Analysis is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another. • A conversion factor is a ratio of equivalent values having different units.

  16. Section 2.2Dimensional Analysis • Writing conversion factors. • Conversion factors are derived from equality relationships, such as 1 dozen eggs=12 eggs. • Percentages can also be used as conversion factor. They relate the number of parts of one component to 100 total parts.

  17. Section 2.2dimensional analysis • Using conversion factors • A conversion factor must cancel one unit and introduce a new one. 32 people x 2bottles x 1eight-pack = 8 eightpacks person 8 bottles

  18. Section 2.3 Uncertainty in Data • Accuracy – how close a measurement is to the true or correct value for the quantity. • Precision – how close a set of measurements for a quantity are to one another, regardless of whether the measurements are correct.

  19. Section 2.3 Uncertainty in Data

  20. Section 2.3 Accuracy and Precision • Error is defined as the difference between an experimental value and an accepted value. • Error=exp value-accepted value • % Error=___ERROR______ x 100 Accepted Value

  21. Section 2.3 Significant Figures • Significant Figures include all known digits plus one estimated digit.

  22. Section 2.3 Significant Figures • Rules for Sig Figs: • Rule 1: Nonzero numbers are always significant. • Rule 2: Zeros between nonzero numbers are always significant. • Rule 3: All final zeros to the right of the decimal are significant. • Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation. • Rule 5: Counting numbers and defined constants have an infinite number of significant figures.

  23. Section 2.3 Rounding Numbers • Calculators are not aware of significant figures. • Answers should not have more significant figures than the original data with the fewest figures, and should be rounded.

  24. Section 2.3Rounding Numbers • Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure. • Rule 2: If the digit to the right of the last significant figure is greater than 5, round up to the last significant figure. • Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up to the last significant figure. • Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up.

  25. Section 2.3Rounding Numbers • Addition and subtraction- • Round numbers so all numbers have the same number of digits to the right of the decimal. • Multiplication and division • Round the answer to the same number of significant figures as the original measurement with the fewest significant figures.

  26. Section 2.4Graphing • All graphing information can be found in your book or from last chapter. You will be responsible for revisiting this information!!!! 

  27. Practice • The 15 members of Mrs. K’s fan club decide to buy caps imprinted with Mrs. K ROCKS! Each cap costs $9.00 and each imprint costs $2.00. To raise money for the caps, the club members decide to sell candy bars at .50 cents each, of which .20 cents is profit. How many bars must you sell to get your cap for free?

  28. Practice Problems 6. Which student’s data are precise? Explain your answer. Student 1: 72.75g, 73.34g, 73.02g, 73.25g Student 2: 72.01g, 71.99g, 72.00g, 71.98g

  29. Practice Problems 7. Using a balance that always reads 0.50 g too low, a student obtained the mass of a beaker to be 50.62 g. The student then added some sugar to the beaker and, using the same blance, obtained a total mass of 69.88 g. The studet recorded the mass of the sugar as 19.26 g. is the mass of the sugar inaccurate by 0.50 gram? Why or Why not?

  30. Practice Problems 8. An experiment performed to determine the density of lead yields a value of 10.95 g/cm³. The literature (true) value for the density of lead is 11.342 g/cm³. Find the percent error.

  31. Practice Problems 9. Find the percent error in a measurement of the boiling point of Br if the laboratory figure (exptl) is 40.6°C and the literature value is 59.35°C.

  32. Practice Problems 4. Which of the units in each of the following pair represents the larger quantity? a. millimeter, centimeter b. picometer, micrometer c. kilogram, centigram d. deciliter, milliliter

  33. Practice Problems 5. A decigram is 0.1 g. Give the name of each of the following quantities. a. 0.001 m b. 0.000 001 s c. 0.01 g d. 0.000 000 000 001 s

  34. Practice Problems 10. How many significant digits are there in each of the following quantities? • 20kg f. 0.004 cm • 0.0051 g g. 0.089 kg • 11m h. 0.00900 L • 0.010 s i. 100.0 °C • 90.4°C j. 20 cars

  35. Calculating Density • A piece of beeswax with a volume of 8.50 cm³ is found to have a mass of 8.06 g. What is the density?

  36. Practice Problems 11. What is the density of a piece of concrete that has a mass of 8.76 g and a volume of 3.07 cm³?

  37. Practice Problems 12. Illegal ivory is sometimes detected on the basis of density. What is the density of a sample of ivory whose volume is 14.5 cm³ and whose mass is 26.8g?

  38. Practice Problems 13. An archeologist finds that a piece of ancient pottery has a mass of 0.61 g and a volume of 0.26 cm³, What is the density of the pottery?

  39. Sample Problem: D to find V Cobalt is a hard magnetic metal that resembles iron in appearance. It has a density of 8.90 g/cm³. What volume would 17.8 g of cobalt have?

  40. Practice Problem 14. Limestone has a density of 2.72 g/cm³. What is the mass of 24.9 cm³ of limestone?

  41. Practice Problems 15. Calcium chloride is used as a deicer on roads in winter. It has a density of 2.50 g/cm³. What is the volume of 7.91 g of this substance?

  42. Sample Problem (calc. skills) • What is the denstiy of a rectangular block of granite of mass 40.4 g and dimensions 2.00 cm by 1.09 cm by 7.04 cm?

  43. Practice Problems 18. Use a calculator to determien the density of a pine board whose demensions are 4.05 cm by 8.85 cm by 164 cm and whose mass is 2580g.

  44. Practice Problems 19. Use a calculator to find the density of a 51.6 g cylindrical steel rod of diameter 0.622 cm and length 22.1 cm.

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